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Use of Lambek's (1958) categorial grammar for linguistic work has generally been rather limited. There appear to be two main reasons for this: the notations most commonly used can sometimes obscure the structure of proofs and fail to clearly convey linguistic structure, and the cMculus as it stands is apparently not powerful enough to describe many phenomena encountered in natural language. In this paper we suggest ways of dealing with both these deficiencies. | PROOF FIGURES AND STRUCTURAL OPERATORS FOR CATEGORIAL GRAMMAR Guy Barry Mark Hepple Neil Leslie and Glyn Morrill Centre for Cognitive Science University of Edinburgh 2 Buccleuch Place Edinburgh EH8 9LW Scotland guyCcogsci.ed.ac.uk mrhCcl.can.ac.uk neilCcogsci.ed.ac.uk Glyn.Morrill et.ruu.nl ABSTRACT Use of Lambck s 1958 categorial grammar for linguistic work has generally been rather limited. There appear to be two main reasons for this the notations most commonly used can sometimes obscure the structure of proofs and fail to clearly convey linguistic structure and the calculus as it stands is apparently not powerful enough to describe many phenomena encountered in natural language. In this paper we suggest ways of dealing with both these deficiencies. Firstly we reformulate Lambek s system using proof figures based on the natural deduction notation commonly used for derivations in logic and discuss some of the related proof-theory. Natural deduction is generally regarded as the most economical and comprehensible system for working on proofs by hand and we suggest that the same advantages hold for a similar presentation of categorial derivations. Secondly we introduce devices called structural modalities based on the structural rules found in logic for the characterization of commutation iteration and optionality. This permits the description of linguistic phenomena which Lambek s system does not capture with the desired sensitivity and generality. LAMBEK CATEGORIAL GRAMMAR PRELIMINARIES Categorial grammar is an approach to language description in which the combination of expressions is governed not by specific linguistic rules but by general logical inference mechanisms. The point of departure can be seen as Frege s position that there are certain complete expressions which are the primary bearers of meaning and that the meanings of incomplete expressions including words are derivative being We would like to thank Hobin Cooper Martin Pickering and Pete Whitelock .
